Решение задач олимпиады

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سؤال

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реши

الإجابة

It looks like you've uploaded several images of questions from an olympiad in Informatics. Let me help you solve them one by one.

Let's start with the first question:

Задание 2 (Question 2)

Question: How many natural numbers xx are there that are greater than the binary number 01111101201111101_2 and less than the hexadecimal number 8F168F_{16}?

To solve this:

  1. Convert 01111101201111101_2 to decimal: 011111012=1251001111101_2 = 125_{10}.

  2. Convert 8F168F_{16} to decimal: 8F16=8×16+15=143108F_{16} = 8 \times 16 + 15 = 143_{10}.

  3. We need to find how many natural numbers are greater than 125 and less than 143. These are the numbers 126 to 142.

  4. Count the numbers: 142126+1=17142 - 126 + 1 = 17.

The answer for this question seems to be missing from the options, so the correct choice would be "Correct answer is missing."


Let me know if you'd like me to proceed with the next question!

سؤال

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реши

Python

python
# Define the adjacency matrix from the table import numpy as np # Adjacency matrix from the image weights = np.array([ [0, 21, 21, 39, 8, 30, 13], [21, 0, 39, 39, 53, 5, 2], [21, 39, 0, 53, 53, 5, 3], [39, 39, 53, 0, 0, 0, 0], [8, 53, 53, 0, 0, 0, 0], [30, 5, 5, 0, 0, 0, 0], [13, 2, 3, 0, 0, 0, 0] ]) # Define edges A-G and B-ZH # Based on the problem, rows and columns need to be matched appropriately # A-G corresponds to vertex 1-7 (adjusting for Python index) # B-ZH corresponds to vertex 2-6 (adjusting for Python index) edge_AG_weight = weights[0, 6] # A-G corresponds to Y1-Y7 edge_BZH_weight = weights[1, 5] # B-ZH corresponds to Y2-Y6 # Calculate total weight total_weight = edge_AG_weight + edge_BZH_weight total_weight

الإجابة

The sum of the weights of the edges АГАГ (A-G) and ВЖВЖ (B-ZH) is 18. Let me know if you'd like further clarification or help with the next question!

سؤال

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дай правильный ответ

الإجابة

Let's go step by step for the task.

Задание 5 (Question 5)

Problem:
We have domino stones set up in a line such that if one stone falls, the others will also fall in sequence. The goal is to determine which stone and in which direction should be pushed to make the maximum number of stones fall.

To solve this:

  1. Initial Table Values: Each domino has an (x, h) pair where x is the position and h is the height.

  2. The Key Insight:
    The stone you push will fall and then trigger other stones to fall, provided the height difference between the current stone and the next is positive (greater height will push the next one). So, we need to check which direction yields the highest number of falling stones.

  3. Calculating the Right Direction:

    • If you push to the right, each stone must be taller than the next for it to fall.
    • If you push to the left, the opposite condition must be true: each stone must be shorter than the previous stone for it to fall.
  4. Solution Strategy: We check each domino and calculate how many stones fall if it is pushed in either direction.

Upon reviewing the question details and calculations, the correct answer appears to be 1, RIGHT, 4.

Let me know if you'd like me to assist further!

سؤال

photo_5278428456922771606_y.jpgphoto_5278428456922771606_y.jpg

дай правильный ответ

الإجابة

Задание 6 (Question 6)

Question:
We need to apply the bitwise OR (|) operation to the numbers 15 and 7.

  1. Convert numbers to binary:

    • 1510=1111215_{10} = 1111_2
    • 710=011127_{10} = 0111_2
  2. Apply bitwise OR (|):

    text
    1111 0111 ---- 1111
  3. Convert back to decimal:

    • 11112=15101111_2 = 15_{10}

Correct answer: 15

سؤال

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дай правильный ответ

الإجابة

Задание 8 (Question 8)

The task is about identifying which algorithm outputs the elements below the main diagonal of a square matrix, based on the flowchart provided.

Let’s break down the flowcharts:

  1. First Flowchart (Algorithm 1):

    • This algorithm seems to work on the rows and columns, and it would visit elements below the main diagonal, which are the elements where row index ii is greater than column index jj.
  2. Second Flowchart (Algorithm 2):

    • This one works similarly but seems to cover the main diagonal itself as well. It doesn’t focus solely on elements below the diagonal.
  3. Third Flowchart (Algorithm 3):

    • This algorithm focuses on visiting all elements below the main diagonal by incrementing the row and column appropriately. It outputs elements strictly below the diagonal.
  4. Fourth Flowchart (Algorithm 4):

    • This one checks all elements including the diagonal, so it wouldn't fit the task.

Answer: The correct algorithms are 1 and 3, as they output elements below the main diagonal.

Let me know if you need further clarification!

سؤال

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реши

الإجابة

Задание 9 (Question 9)

We need to evaluate the following set operation:

A(BC)A \cap (B \cup C)

Where:

  • A={1,a,b}A = \{1, a, b\}
  • B={c,d,e}B = \{c, d, e\}
  • C={5,a,b}C = \{5, a, b\}
  • U={1,2,3,4,5,a,b,c,d,e}U = \{1, 2, 3, 4, 5, a, b, c, d, e\}

Step-by-Step Solution:

  1. Find BCB \cup C (Union of B and C):

    BC={c,d,e}{5,a,b}={c,d,e,5,a,b}B \cup C = \{c, d, e\} \cup \{5, a, b\} = \{c, d, e, 5, a, b\}
  2. Find A(BC)A \cap (B \cup C) (Intersection of A and BCB \cup C):

    A(BC)={1,a,b}{c,d,e,5,a,b}={a,b}A \cap (B \cup C) = \{1, a, b\} \cap \{c, d, e, 5, a, b\} = \{a, b\}

Answer: {a, b}

The correct option is (a,b,c,e).

Let me know if you'd like further clarification!

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